Now it's been a while.. But I'm guessing the nature of an empire is similar to the nature of an animal or human. Like human nature, is our human tendencies. So in a similar fashion, the nature of an empire would be the tendencies of an empire: were they more trade based? More war-oriented? Was the emperor benevolent? Did it have good relations with others? When it conquered did it leave the original ruler in place and not force a culture change? Or was it completely the opposite? What was the culture like?

I answered your questions with more questions... But hopefully it'll help you